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2006 | 4 | 1 | 82-109

Tytuł artykułu

Blow-up of regular submanifolds in Heisenberg groups and applications

Treść / Zawartość

Warianty tytułu

Języki publikacji

EN

Abstrakty

EN
We obtain a blow-up theorem for regular submanifolds in the Heisenberg group, where intrinsic dilations are used. Main consequence of this result is an explicit formula for the density of (p+1)-dimensional spherical Hausdorff measure restricted to a p-dimensional submanifold with respect to the Riemannian surface measure. We explicitly compute this formula in some simple examples and we present a lower semicontinuity result for the spherical Hausdorff measure with respect to the weak convergence of currents. Another application is the proof of an intrinsic coarea formula for vector-valued mappings on the Heisenberg group.

Wydawca

Czasopismo

Rocznik

Tom

4

Numer

1

Strony

82-109

Opis fizyczny

Daty

wydano
2006-03-01
online
2006-03-01

Twórcy

Bibliografia

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  • [3] A. Bellaïche and J.J. Risler (Eds.): Sub-Riemannian geometry, Progress in Mathematics, Vol. 144, Birkhäuser Verlag, Basel, 1996.
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  • [7] B. Franchi, R. Serapioni and F. Serra Cassano: “Meyers-Serrin type theorems and relaxation of variational integrals depending on vector fields”, Houston Jour. Math., Vol. 22, (1996), pp. 859–889.
  • [8] B. Franchi, R. Serapioni and F. Serra Cassano: “Rectifiability and Perimeter in the Heisenberg group”, Math. Ann., Vol. 321(3), (2001).
  • [9] B. Franchi, R. Serapioni and F. Serra Cassano: “Regular hypersurfaces, intrinsic perimeter and implicit function theorem in Carnot groups”, Comm. Anal. Geom., Vol. 11(5), (2003), pp. 909–944.
  • [10] B. Franchi, R. Serapioni and F. Serra Cassano: Regular submanifolds, graphs and area formula in Heisenberg groups, preprint, (2004).
  • [11] M. Gromov: “Carnot-Carathéodory spaces seen from within”, In: A. Bellaiche and J. Risler (Eds.): Subriemannian Geometry, Progress in Mathematics, Vol. 144, Birkhauser Verlag, Basel, 1996.
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  • [14] B. Kirchheim and F. Serra Cassano: “Rectifiability and parametrization of intrinsic regular surfaces in the Heisenberg group”, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5), Vol. 3(4), (2004), pp. 871–896.
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  • [16] I. Kupka: “Géométrie sous-riemannienne”, Astérisque, Vol. 241(817,5), (1997), pp. 351–380.
  • [17] V. Magnani: “Differentiability and Area formula on stratified Lie groups”, Houston Jour. Math., Vol. 27(2), (2001), pp. 297–323.
  • [18] V. Magnani: “On a general coarea inequality and applications”, Ann. Acad. Sci. Fenn. Math., Vol. 27, (2002), pp. 121–140.
  • [19] V. Magnani: “A Blow-up Theorem for regular hypersurfaces on nilpotent groups”, Manuscripta Math., Vol. 110(1), (2003), pp. 55–76. http://dx.doi.org/10.1007/s00229-002-0303-y
  • [20] V. Magnani: “The coarea formula for real-valued Lipschitz maps on stratified groups”, Math. Nachr., Vol. 278(14), (2005), pp. 1–17. http://dx.doi.org/10.1002/mana.200310334
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  • [22] V. Magnani: “Characteristic points, rectifiability and perimeter measure on stratified groups”, J. Eur. Math. Soc., to appear.
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  • [28] N.Th. Varopoulos, L. Saloff-Coste and T. Coulhon: Analysis and Geometry on Groups, Cambridge University Press, Cambridge, 1992.

Typ dokumentu

Bibliografia

Identyfikatory

Identyfikator YADDA

bwmeta1.element.doi-10_1007_s11533-005-0006-1
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